Determine that a and b are orthogonal,

where a = 2i + 3j - 2k, and b = 4i + 2j + 7k.

If two vectors are orthogonal, the angle between them is 90° , making the cosine of the angle between them 0.

If two vectors are parallel, the angle between them is either 0° or 180° , making the cosine of the angle between them 1 or -1.

Hence, we proceed by finding the cosine of that angle:

. Here this becomes

The two vectors must have a 90° angle between them.